Tag Archives: varieties

In this article, we will consider algebraic geometry in the projective space. Throughout this article, k denotes an algebraically closed field. Projective Space Definition. Let . On the set , we consider the equivalence relation: The projective n-space is the set … Continue reading →

Torsion and Flatness Definition. Let A be a ring and M an A-module; let . If satisfies , we call it an –torsion element. If is an -torsion for some non-zero-divisor we call it a torsion element. M is said … Continue reading →

Coordinate Rings as k-algebras Let k be an algebraically closed field. Recall that a closed subset is identified by its coordinate ring k[V], which is a finitely generated k-algebra since Definition. An affine k-variety is a finitely generated k-algebra A which is … Continue reading →